login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035194 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 12. 21

%I

%S 1,1,1,1,0,1,0,1,1,0,2,1,2,0,0,1,0,1,0,0,0,2,2,1,1,2,1,0,0,0,0,1,2,0,

%T 0,1,2,0,2,0,0,0,0,2,0,2,2,1,1,1,0,2,0,1,0,0,0,0,2,0,2,0,0,1,0,2,0,0,

%U 2,0,2,1,2,2,1,0,0,2,0,0,1

%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 12.

%C Coefficients of Dedekind zeta function for the quadratic number field of discriminant 12. See A002324 for formula and Maple code. - _N. J. A. Sloane_, Mar 22 2022

%H G. C. Greubel, <a href="/A035194/b035194.txt">Table of n, a(n) for n = 1..10000</a>

%t a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[12, #] &]]; Table[ a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 27 2018 *)

%o (PARI) m=12; direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

%Y Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.

%Y Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.

%K nonn

%O 1,11

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 22:33 EDT 2022. Contains 353993 sequences. (Running on oeis4.)